On Graded Classical S-Primary Submodules

Abstract

The purpose of this article is to introduce the graded classical S-primary submodules which are extensions of graded classical primary submodules. We state that P is a graded classical S-primary submodule of R-module M if there exists $s\in S$ such that $x,y\in h(R)$ and $m\in h(M)$, if $xym\in P$, then $sxm\in P$ or $s{y}^{n}m\in P$ for some positive integer n. Several properties and characteristics of graded classical S-primary submodules have been studied.